Elimination of vibration localization in mistuned periodic structures

In this note, mistuned periodic structures are considered. Due to mistunings, some components of such structures may vibrate with small amplitudes, while some other components may vibrate with significantly large amplitudes. Such a behavior is known as vibration localization and is undesirable. To have a means of determining the occurrence of vibration localization, a sensitivity matrix is defined. This matrix and its singular values are computable. It is argued that if some of the singular values of the sensitivity matrix are large, then vibration localization can possibly occur. More importantly, an effective passive technique is proposed that eliminates vibration localization in mistuned periodic structures. The technique is to add small components between the structure components. Using the sensitivity matrix, it is shown that the added components indeed eliminate vibration localization.